Isotropic materials have equal physical properties along all axes and are not birefringent. As such, light waves entering the isotropic material are not split into light waves of differing velocities. Accordingly, isotropic materials have a single index of refraction .eta..
In contrast, anisotropic materials have unequal physical properties along different axes. Optically anisotropic materials are typically birefringent. That is, light waves are split upon entry into the anisotropic material into two waves with differing velocities, and therefore, different refractive indices (e.g., .eta..sub.1 and .eta..sub.2). An example of an optically anisotropic material is an oriented polyester polymer film.
An optical characteristic of an anisotropic material is optical retardation. Optical retardation is defined as the product of thickness and birefringence. More particularly: EQU R=t*birefringence Equation 1
Written alternatively, EQU R=t*(.eta..sub.1 -.eta..sub.2) Equation 2
wherein:
t is thickness, PA1 .eta..sub.1 is the index of refraction in a first direction, and PA1 .eta..sub.2 is the index of refraction in a second direction perpendicular to the first direction.
U.S. Pat. Nos. 5,659,392 and No. 5,596,409 (Marcus et al), commonly assigned and incorporated herein by reference, teach an apparatus and method for measuring the physical properties of an object, such as thickness, group index of refraction, and distance to a surface. The apparatus includes a non-coherent light interferometer in association with a coherent light interferometer.
Non-coherent light interferometry has been used to measure physical properties of a material. For example, U.S. Pat. No. 5,610,716 (Sorin et al) relates to an apparatus and method for measuring thickness of a film of an isotropic material using an interferometer. The film thickness is obtained by determining the distance between two packets in the output of the interferometer. As referenced by Sorin to a "group index equal to .eta.", the apparatus and method of Sorin et al is directed to an isotropic material. In addition, Sorin refers only to the measurement of thickness. As such, Sorin et al does not address measuring optical retardation since Sorin et al is not directed to anisotropic materials.
Apparatus and methods exist for determining the birefringence of a material. For example, German Patent No. DE 23 38 305 C3 (Frangen) discloses a method for determining the linear birefringence of a material, particularly in a form suitable for use in process control. Using transmission, Frangen teaches a first polarizer upstream of the material, and a second polarizer downstream of the material whose plane of polarization is perpendicular to that of the first polarizer. A photoelectrical receiving unit downstream of the second polarizer detects the wavelengths to determine birefringence. A separate thickness measuring device is provided. However, it may be desired to determine only retardation, and not the specific values of thickness and/or birefringence. Therefore, while the German apparatus may have achieved a certain level of success, it affords a complex solution to the measurement of retardation. Further, it may be desirable to determine retardation without the use of polarizing optics.
As such, a need continues to exist for a method for determining the optical retardation of an anisotropic material. The retardation should be measured directly, that is, without determining the specific values of thickness and birefringence. A suitable apparatus is preferably simple in design, transportable, compact in size, and does not utilize polarizing optics. A suitable method is robust, consistent, and provides analysis results quickly.